I think the 'adventure game'-description is definitely the best. Storytelling game conjures up images of people sitting around a campfire, taking turns to add new parts to a story. Not everyone can do that or wants to do that.
The primary reason to play any RPG is to have fun - on that, everyone agrees. What constitutes fun is different for almost everyone.
For me, and for most people I played with, playing a game which had the characters as the lead heroes in a strong plot was ultimately most rewarding. The 'trouble' with D&D (or the defining characteristic) is that it basically took a part of LOTR (the mines of moria) and developed that into the archetypal RPG experience: a diverse group enters a 'hole in the ground', discovers all kinds of monstrous enemies, and ends up facing a boss monster/NPC. It's a very limited paradigm on the one hand, on the other it's clear and it allows for an infinite amount of variations in the details. However, as a story experience it is unfulfilling IMHO, especially if it is repeated ad nauseam. As a tactical exercise, it can remain fun, especially due to the enormous number of variables which change every time (monsters, traps, new abilities of PCs, in some cases the backstory to the adventure).
The main hurdle to telling novel- or movielike stories in D&D is the experience mechanism. You have to accumulate a large number of XPs to progress. Therefore, as an adventure designer you are forced to send huge numbers of opponents to be defeated by the PCs, or their progress will be too slow. Most D&D modules contain absurd numbers of opponents (something which was ported to most CRPGs).
On the other hand, where a short story may get away with introducing one monster, and a novel with a handful of weird creatures, monsters lose most of their mystique in D&D because they are basically XP generators. No RAW D&D adventure could get away with introducing only one monster, which has very special powers and/or weaknesses which the characters must discover and exploit. In other fantasy games this would however be a perfectly valid and probably memorable scenario - Fantasy HERO, for example, or even Conan d20 - both games in which the experience factor is handled quite differently, or Warhammer, or BRP. (Conan proposes a very freeform type of XP gain, in which the GM decides after a number of adventures to raise the level of the PCs).
The other big storytelling hurdle, and the one which leads to railroading on both the part of the adventure designer and the DM, is the fact that the protagonists of the tale (PCs) have free will and at times will completely derail the intended plot. Case in point, when I was playing in Shadows over Bögenhaven, as a halfling thief, my character pretended to be a merchant to glean some necessary info. One thing led to another, and before long I was getting ready to open a trading house... great fun, it turned out, but not what the GM and module had in mind (not to mention the rest of the group). So I had to shut the shop down, for the greater good...
Actually, the storytelling aspect of RPGs is best realized in very small groups, ideally one player and one GM. As both are there to have fun, the player will generally be far less inclined to deliberately run off the (more or less) intended track. I've played CN3 like this (using Rolemaster), and it worked a treat, just like several Flashing Blades adventures and - best of all, probably - the James Bond modules for Victory Games (though I played them with a heavily houseruled version of Top Secret 1st. ed.). In these games, the plot was clear, the PC had a natural inclination to follow the trail of the plot, and in general, a great time was had by both.
Changing this to a group experience is not impossible, but far more difficult. And it may definitely conflict with the concept of fun of many gamers (especially those who love the entire D&D paradigm as is).
The primary reason to play any RPG is to have fun - on that, everyone agrees. What constitutes fun is different for almost everyone.
For me, and for most people I played with, playing a game which had the characters as the lead heroes in a strong plot was ultimately most rewarding. The 'trouble' with D&D (or the defining characteristic) is that it basically took a part of LOTR (the mines of moria) and developed that into the archetypal RPG experience: a diverse group enters a 'hole in the ground', discovers all kinds of monstrous enemies, and ends up facing a boss monster/NPC. It's a very limited paradigm on the one hand, on the other it's clear and it allows for an infinite amount of variations in the details. However, as a story experience it is unfulfilling IMHO, especially if it is repeated ad nauseam. As a tactical exercise, it can remain fun, especially due to the enormous number of variables which change every time (monsters, traps, new abilities of PCs, in some cases the backstory to the adventure).
The main hurdle to telling novel- or movielike stories in D&D is the experience mechanism. You have to accumulate a large number of XPs to progress. Therefore, as an adventure designer you are forced to send huge numbers of opponents to be defeated by the PCs, or their progress will be too slow. Most D&D modules contain absurd numbers of opponents (something which was ported to most CRPGs).
On the other hand, where a short story may get away with introducing one monster, and a novel with a handful of weird creatures, monsters lose most of their mystique in D&D because they are basically XP generators. No RAW D&D adventure could get away with introducing only one monster, which has very special powers and/or weaknesses which the characters must discover and exploit. In other fantasy games this would however be a perfectly valid and probably memorable scenario - Fantasy HERO, for example, or even Conan d20 - both games in which the experience factor is handled quite differently, or Warhammer, or BRP. (Conan proposes a very freeform type of XP gain, in which the GM decides after a number of adventures to raise the level of the PCs).
The other big storytelling hurdle, and the one which leads to railroading on both the part of the adventure designer and the DM, is the fact that the protagonists of the tale (PCs) have free will and at times will completely derail the intended plot. Case in point, when I was playing in Shadows over Bögenhaven, as a halfling thief, my character pretended to be a merchant to glean some necessary info. One thing led to another, and before long I was getting ready to open a trading house... great fun, it turned out, but not what the GM and module had in mind (not to mention the rest of the group). So I had to shut the shop down, for the greater good...

Actually, the storytelling aspect of RPGs is best realized in very small groups, ideally one player and one GM. As both are there to have fun, the player will generally be far less inclined to deliberately run off the (more or less) intended track. I've played CN3 like this (using Rolemaster), and it worked a treat, just like several Flashing Blades adventures and - best of all, probably - the James Bond modules for Victory Games (though I played them with a heavily houseruled version of Top Secret 1st. ed.). In these games, the plot was clear, the PC had a natural inclination to follow the trail of the plot, and in general, a great time was had by both.
Changing this to a group experience is not impossible, but far more difficult. And it may definitely conflict with the concept of fun of many gamers (especially those who love the entire D&D paradigm as is).